具有相依变量成批到达排队系统等待时间的注记

A Note on the Waiting Times for Bulk Arrival Queues with Dependent Variables

研究了成批到达排队系统G(X)/G/1的基本变量具有相依关系时,等待时间的随机比较性质.证明了当到达批量与到达间隔的相依关系越强时,相应的等待时间越短;当服务时间和到达间隔的相依关系越强时,相应的等待时间越短.同时探讨了基本变量相依时成批到达排队系统的等待时间的界.

We consider single-server bulk arrivals queues G（X）/G/1with the dependence between group sizes and inter-arrival times of customers and between service times and inter-arrival times,respectively.In these two cases,we show that stronger dependence between them leads to shorter waiting times in the increasing convex ordering sense.We also obtain bounds of waiting times in bulk arrival queues.